Results 1 to 7 of 7

Thread: Please check my answer (integral calculus)

  1. #1
    Newbie
    Joined
    Jun 2017
    From
    Australia
    Posts
    9

    Please check my answer (integral calculus)

    I've attached the question as an image here:

    Please check my answer (integral calculus)-quesiton2.png

    For a) I get 9 square units

    and b) I get (243pi)/5 cube units

    Help would be much appreciated
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,925
    Thanks
    2491

    Re: Please check my answer (integral calculus)

    a) is correct

    I'd be interested in seeing your work for (b). I don't know how you arrived at that answer.

    Consider a infinitesimal cross section of the solid between $(x,x+dx)$

    It's a circular disk of radius $\sqrt{x}$ and thickness $dx$

    Thus it's differential volume is

    $dV = \pi (\sqrt{x})^2~dx = \pi x~dx$

    $V = \displaystyle \int_0^9~dV = \displaystyle \int_0^9~\pi x = \left . \pi \dfrac{x^2}{2} \right|_0^9 = \dfrac{81\pi}{2}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2017
    From
    Australia
    Posts
    9

    Re: Please check my answer (integral calculus)

    Hi Romsek,

    Thanks for the reply! Unfortunately I'm confused by the method you've shown as my level of maths is not very advanced as of yet. I'll upload an image of my working using the method I've been shown. Perhaps you could point out what I've done incorrectly?

    Please check my answer (integral calculus)-math1.jpg
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,925
    Thanks
    2491

    Re: Please check my answer (integral calculus)

    Quote Originally Posted by Quoctopus View Post
    Hi Romsek,

    Thanks for the reply! Unfortunately I'm confused by the method you've shown as my level of maths is not very advanced as of yet. I'll upload an image of my working using the method I've been shown. Perhaps you could point out what I've done incorrectly?

    Click image for larger version. 

Name:	math1.jpg 
Views:	11 
Size:	967.1 KB 
ID:	38139
    Bah, my answer was when the initial curve is rotated about the x-axis.

    Let me redo this and get back to you.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,925
    Thanks
    2491

    Re: Please check my answer (integral calculus)

    Ok.

    Consider a cross section of the volume at height $z$ with thickness $dz$

    This circular disk has radius $r=z^2$ and $z \in [0,3]$

    $dV = \pi r^2~dz = \pi z^4~dz$

    $V = \displaystyle \int_0^3 dV = \int_0^3 \pi z^4 ~dz = \dfrac{243\pi}{5}$

    So you were right all along. My apologies.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2017
    From
    Australia
    Posts
    9

    Re: Please check my answer (integral calculus)

    Thanks for that no need to apologise
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,466
    Thanks
    2893

    Re: Please check my answer (integral calculus)

    romsek's first calculation has the figure rotated around the x-axis rather than the y-axis.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. calculus answer check
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Apr 18th 2011, 05:32 PM
  2. Answer check (triple integral)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 23rd 2009, 05:58 AM
  3. Double integral answer check.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Apr 8th 2009, 06:08 AM
  4. Check answer for this difinate integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jun 3rd 2008, 08:17 PM
  5. Calculus problem : Check my answer
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jun 2nd 2006, 05:56 AM

/mathhelpforum @mathhelpforum